Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

A free weekly iron-folic acid supplementation and regular deworming program is associated with improved hemoglobin and iron status indicators in Vietnamese women

Background Anemia due to iron deficiency is recognized as one of the major nutritional deficiencies in women and children in developing countries. Daily iron supplementation for pregnant women is recommended in many countries although there are few reports of these programs working efficiently or effectively. Weekly iron-folic acid supplementation (WIFS) and regular deworming treatment is recommended for non-pregnant women living in areas with high rates of anemia. Following a baseline survey to assess the prevalence of anemia, iron deficiency and soil transmitted helminth infections, we implemented a program to make WIFS and regular deworming treatment freely and universally available for all women of reproductive age in two districts of a province in northern Vietnam over a 12 month period. The impact of the program at the population level was assessed in terms of: i) change in mean hemoglobin and iron status indicators, and ii) change in the prevalence of anemia, iron deficiency and hookworm infections. Method Distribution of WIFS and deworming were integrated with routine health services and made available to 52,000 women. Demographic data and blood and stool samples were collected in baseline, and three and 12-month post-implementation surveys using a population-based, stratified multi-stage cluster sampling design. Results The mean Hb increased by 9.6 g/L (95% CI, 5.7, 13.5, p < 0.001) during the study period. Anemia (Hb<120 g/L) was present in 131/349 (37.5%, 95% CI 31.3, 44.8) subjects at baseline, and in 70/363 (19.3%, 95% CI 14.0, 24.6) after twelve months. Iron deficiency reduced from 75/329 (22.8%, 95% CI 16.9, 28.6) to 33/353 (9.3%, 95% CI 5.7, 13.0) by the 12-mnth survey, and hookworm infection from 279/366 (76.2%,, 95% CI 68.6, 83.8) to 66/287 (23.0%, 95% CI 17.5, 28.5) over the same period. Conclusion A free, universal WIFS program with regular deworming was associated with reduced prevalence and severity of anemia, iron deficiency and ho

Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Crisis communication under transformative change : the emergent context and roles of primary and secondary organisations

In an era of complex challenges that draw sustained media attention and entangle multiple organisational actors, this thesis addresses the gap between current trends in society and business, and existing scholarship in public relations and crisis communication. By responding to calls from crisis communication researchers to develop theory (Coombs, 2006a), to examine the interdependencies of crises (Seeger, Sellnow, & Ulmer, 1998), and to consider variation in crisis response (Seeger, 2002), this thesis contributes to theory development in crisis communication and public relations. Through transformative change, this thesis extends existing scholarship built on a preservation or conservation logic where public relations is used to maintain stability by incrementally responding to changes in an organisation‘s environment (Cutlip, Center, & Broom, 2006; Everett, 2001; Grunig, 2000; Spicer, 1997). Based on the opportunity to contribute to ongoing theoretical development in the literature, the overall research problem guiding this thesis asks: How does transformative change during crisis influence corporate actors’ communication? This thesis adopts punctuated equilibrium theory, which describes change as alternating between long periods of stability and short periods of revolutionary or transformative change (Gersick, 1991; Romanelli & Tushman, 1994; Siggelkow, 2002; Tushman, Newman, & Romanelli, 1986; Tushman & Romanelli, 1985). As a theory for change, punctuated equilibrium provides an opportunity to examine public relations and transformative change, building on scholarship that is based primarily on incremental change. Further, existing scholarship in public relations and crisis communication focuses on the actions of single organisations in situational or short-term crisis events. Punctuated equilibrium theory enables the study of multiple crises and multiple organisational responses during transformative change. In doing so, punctuated equilibrium theory provides a framework to explain both the context for transformative change and actions or strategies enacted by organisations during transformative change (Tushman, Newman, & Romanelli, 1986; Tushman & Romanelli, 1985; Tushman, Virany, & Romanelli, 1986). The connections between context and action inform the research questions that guide this thesis: RQ1: What symbolic and substantive strategies persist and change as crises develop from situational events to transformative and multiple linked events? RQ2: What features of the crisis context influence changes in symbolic and substantive strategies? To shed light on these research questions, the thesis adopts a qualitative approach guided by process theory and methods to explicate the events, sequences and activities that were essential to change (Pettigrew, 1992; Van de Ven, 1992). Specifically, the thesis draws on an alternative template strategy (Langley, 1999) that provides several alternative interpretations of the same events (Allison, 1971; Allison & Zelikow, 1999). Following Allison (1971) and Allison and Zelikow (1999), this thesis uses three alternative templates of crisis or strategic response typologies to construct three narratives using media articles and organisational documents. The narratives are compared to identify and draw out different patterns of crisis communication strategies that operate within different crisis contexts. The thesis is based on the crisis events that affected three organisations within the pharmaceutical industry for four years. The primary organisation is Merck, as its product recall crisis triggered transformative change affecting, in different ways, the secondary organisations of Pfizer and Novartis. Three narratives are presented based on the crisis or strategic response typologies of Coombs (2006b), Allen and Caillouet (1994), and Oliver (1991). The findings of this thesis reveal different stories about crisis communication under transformative change. By zooming in to a micro perspective (Nicolini, 2009) to focus on the crisis communication and actions of a single organisation and zooming out to a macro perspective (Nicolini, 2009) to consider multiple organisations, new insights about crisis communication, change and the relationships among multiple organisations are revealed at context and action levels. At the context level, each subsequent narrative demonstrates greater connections among multiple corporate actors. By zooming out from Coombs‘ (2006b) focus on single organisations to consider Allen and Caillouet‘s (1994) integration of the web of corporate actors, the thesis demonstrates how corporate actors add accountability pressures to the primary organisation. Next, by zooming further out to the macro perspective by considering Oliver‘s (1991) strategic responses to institutional processes, the thesis reveals a greater range of corporate actors that are caught up in the process of transformative change and accounts for their varying levels of agency over their environment. By zooming in to a micro perspective and out to a macro perspective (Nicolini, 2009) across alternative templates, the thesis sheds light on sequences, events, and actions of primary and secondary organisations. Although the primary organisation remains the focus of sustained media attention across the four-year time frame, the secondary organisations, even when one faced a similar starting situation to the primary organisation, were buffered by the process of transformative change. This understanding of crisis contexts in transforming environments builds on existing knowledge in crisis communication. At the action level, the thesis also reveals different interpretations from each alternative template. Coombs‘ (2006b) narrative shows persistence in the primary organisation‘s crisis or strategic responses over the four-year time frame of the thesis. That is, the primary organisation consistently applies a diminish crisis response. At times, the primary organisation drew on denial responses when corporate actors questioned its legitimacy or actions. To close the crisis, the primary organisation uses a rebuild crisis posture (Coombs, 2006). These finding are replicated in Allen and Caillouet‘s (1994) narrative, noting this template‘s limitation to communication messages only. Oliver‘s (1991) narrative is consistent with Coombs‘ (2006b) but also demonstrated a shift from a strategic response that signals conformity to the environment to one that signals more active resistance to the environment over time. Specifically, the primary organisation‘s initial response demonstrates conformity but these same messages were used some three years later to set new expectations in the environment in order to shape criteria and build acceptance for future organisational decisions. In summary, the findings demonstrate the power of crisis or strategic responses when considered over time and in the context of transformative change. The conclusions of this research contribute to scholarship in the public relations and management literatures. Based on the significance of organisational theory, the primary contribution of the theory relates to the role of interorganisational linkages or legitimacy buffers that form during the punctuation of equilibrium. The network of linkages among the corporate actors are significant also to the crisis communication literature as they form part of the process model of crisis communication under punctuated equilibrium. This model extends existing research that focuses on crisis communication of single organisations to consider the emergent context that incorporates secondary organisations as well as the localised contests of legitimacy and buffers from regulatory authorities. The thesis also provides an empirical base for punctuated equilibrium in public relations and crisis communication, extending Murphy‘s (2000) introduction of the theory to the public relations literature. In doing this, punctuated equilibrium theory reinvigorates theoretical development in crisis communication by extending existing scholarship around incrementalist approaches and demonstrating how public relations works in the context of transformative change. Further research in this area could consider using alternative templates to study transformative change caused by a range of crisis types from natural disasters to product tampering, and to add further insight into the dynamics between primary and secondary organisations. This thesis contributes to practice by providing guidelines for crisis response strategy selection and indicators related to the emergent context for crises under transformative change that will help primary and secondary organisations‘ responses to crises.

Stochastic models and simulation of ion channel dynamics

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.